There are now four models that I have tested with this data. The first model is a simple HMM that is event driven: activities are only allowed to switch when a tag is seen. This is called the "Untimed" Model.
The second model is a simple HMM that is clock driven: activities are allowed to switch on every clock tick whether or not a tag is seen. I'm calling this the "Timed" Model. In fact it enforces an exponential distribution on the activities just by the nature of the self transition.
The third model is an HMM that is also clock driven, but I add a countdown variable to enforce a different distribution that an exponential distribution. In this case I enforce a gamma distribution.
The final model is an HMM in which each activity is a three state sequence. I train each activity separately to get an implicit gamma distribution (negative binomial).

In the first three cases to model this domain with HMMs I segmented each of the traces into their 12 composite activities. I calculated P(RFID objects given activity). In the timed cases I added a null observation for each second in which there was no RFID observation. Then I constructed an HMM in which there was one node for each activity. Each node has a self-transition whose probability was calculated based on mean duration (exponential timed case) or mean number of observations per activity (untimed case). In the gamma case the "D"uration varable governs the "A"ctivity state switches. Each "A"ctivity state can transition to any of the other 13 states with a uniform probability. The HMMs start with a uniform prior over all of the activities. I then performed 17 fold cross-validation on the user traces and determined the viterbi path through the state space that corresponded to left out user trace.

For the gamma distribution I used the DBN on the left to do inference. Since I'm using a plain vanilla viterbi algorithm I create the full |A|x|D| state space to represent the world. "A" is the Activity that is being performed. "D" is the number of seconds left in the activity. Normally "A" stays the same from time to time+1, and "D" counts down deterministically. When "D" reaches 0, "A" is chosen uniformly from the next possible activities. Then "D" is chosen according the gamma distribution associated with the new "A". Then I do exact inference to explain the observed tag sequence and recover the optimal state path through time.